How to copy movements from one object to another?
Give a look here.
Basically you can link some properties (one of them is animation) from an object to some other object by selecting all the object (the object that has the animation needs to be the active, so select it at last), then pressing CTRL+L.
A dropdown menu will appear. There you can select which property to link from the active object to all the selected (but not active) objects.